def fin_v

bend-collections-laws-crypto@1.0.0.0 · proofs/crypto/secp256k1/psign.bend:133

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/field.bend as FS
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/curve.bend as CV
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/secp256k1/ecdsa.bend as ES
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/scalar.bend as S
import bend-collections-laws-crypto@1.0.0.0/src/crypto/secp256k1/ecdsa.bend as E
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/point.bend as PT
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/sel.bend as SL
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/secp256k1/pscal.bend as SQ

133def fin_v(+one: Nat, +h1: {one == 1n : Nat}, +z: List<&2, Nat>, +hz: {FS.reduced(one, FS.order(one), z) == True{} : Bool}, +d: List<&2, Nat>, +hd: {FS.reduced(one, FS.order(one), d) == True{} : Bool}, +k: List<&2, Nat>, +hk: {FS.reduced(one, FS.order(one), k) == True{} : Bool}, +x: List<&2, Nat>, +hx: {PT.red(one, x) == True{} : Bool}, +y: List<&2, Nat>) -> {matt(E.finish(z, d, k, x, y)) == ES.finish(one, FS.value(one, z), FS.value(one, d), FS.value(one, k), CV.SAffine{FS.value(one, x), FS.value(one, y)}) : ES.Attempt}:
134  +hlx = SL.l16(one, x, hx)
135  fin_g(one, h1, S.reduce(x), SQ.sred_r(one, h1, x, hlx), S.mul(S.inv(k), S.add(z, S.mul(S.reduce(x), d))), s0_r(one, h1, z, hz, d, hd, k, hk, x, hlx), x, y, Nat.mod(FS.value(one, x), FS.order(one)), SQ.sred_v(one, h1, x, hlx), FS.mmul(FS.order(one), FS.minv(FS.order(one), FS.value(one, k)), FS.madd(FS.order(one), FS.value(one, z), FS.mmul(FS.order(one), Nat.mod(FS.value(one, x), FS.order(one)), FS.value(one, d)))), s0_v(one, h1, z, hz, d, hd, k, hk, x, hlx))